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XAU Volume: Will the real volume please stand up? |
Introduction
Do you remember the TV show "What's My Line"? If not, don't worry. The show had three panelists who played 20 questions with an unknown remarkable guest and two imposters. The guest may have been an inventor or a farmer, it didn't matter. However the panelists had to figure out who was the guest and after the panelists made their choice, they asked, "will the real guest stand up?"
The question facing technical analysis today is not so much finding a new indicator but deciding on which data set to use. This issue recently showed the ugly side of technical analysis with the XAU index. It's ugly because the ambiguity raised in this article demonstrates why technical analysis has a long way towards becoming a science. The problem stems from poor standards and definitions. It also is exacerbated by technicians who are not paying attention to details and inappropriately mixing data sets. It is common for technicians to use end of day quotations that represent an aggregate total of all trades from all US exchanges, but then they compare the quotes from individual stocks to quotes from sector indices, which aren't using the same exchange data. They assume that the data is correct because they assume that it originated from the exchange. But in the case of the XAU, it doesn't. The Philadelphia Stock Exchange does not report a total volume figure for the XAU. However, there are two major internet sources that do, and they are interestingly using different definitions for the reporting of index values versus the reporting of stock quotations.
Bloomberg.com provides an XAU volume figure but it only totals the trading volume from the individual component stocks trading on the stock's primary exchange during regular trading hours (RTH). In contrast, Bloomberg.com provides stock quotations that use a different definition. Their stock quotes include trading volume from all US exchanges, which includes pre-market and after-market trading volume.
Another major web source for quotes is Yahoo. This web portal provides pricing information and up until recently it provided volume information in the historical quote section. It still displays volume information on the XAU chart. The only problem was that it is reporting the Philadelphia Exchange's total daily volume and not the XAU's volume. At least this has been rectified in the historical quote area of Yahoo's quote service, but the charts for the XAU still show the Philadelphia Exchange's total daily volume. It's disturbing that Yahoo doesn't disclose the composition of the quote and it is misleading many investors and technicians. This is particularly important because the index recently changed from eleven stocks to twelve. So will the real XAU volume stand up?
Typically when stocks are concerned, the trading volume should be a simple matter. And to the non-professional, a small investor doesn't understand why there are so many different quotations out there. To the average investor it's black and white, there's only one quotation. But unfortunately, there isn't. As the world of finance has moved to 24 hour trading each exchange provides a record of all its transactions and they can all be slightly different. Then depending on which data vendor you use, your data vendor will purchase access to these quotes and combine them in different ways because, after all, the customer only wants one quote for the day. It could be that your data vendor just simply passes the data through to you or it combines information from several exchanges and then sends it to you. The vendor could also have several agreements with various data vendors who collate and compile quotations differently. The issue is how are you to know. All you know is that you're getting a quote but did you ask what is its composition? In either case, somewhere after the information leaves the exchange, data vendors are modifying it to fit into their data stream and nobody is asking how this quotation is being constructed or aggregated. It's a quote.
It's no surprise that market technicians are puzzled when they try to create and apply rules only to find out that what works for stocks doesn't work for indices. Another consequence it that technical analysis will lose credibility if everybody applies the same rules and arrives at different conclusions because everybody is analyzing different data. In the end, investors and clients will lose interest when differing views are presented. This is all the result of using different data sets and not precisely identifying it or disclosing its classification.
This has even created confusion in the ranks of professionals and there's one organization www.ta-lib.org that is trying to address another issue with regards to data and that has to do with naming conventions. This organization is trying to standardize naming conventions so that investors don't have to memorize three different symbols for three different data services for one issue, and programmers don't need to spend hours building databases which cross reference the various symbols from different sources.
The remedy is simple. At least state which data set you are using so that other professionals and investors can duplicate your findings. This will go a long way towards improving the field of technical analysis because everybody will at least start with the same data and arrive at the same conclusion. And so the problem of analyzing the XAU's volume is illustrated below.
Five methods to calculate Volume
The XAU recently made a change in both the number of stocks in the index and the companies in it. This isn't the first time a change has been made, but in this instance, the change occurred coincidentally at a critical juncture in using the Wykoff method of swing trading. As you'll see, depending upon which volume graph you use the outcome will be dramatically different. In one case, you'll be a buyer of the dips and in the other case you'll be a seller of the highs. So how's an investor to know which scenario is correct? Or worse yet, which one will the professional analyst pick, who will steer countless investors down the wrong path?
I have constructed several graphs to illustrate the problem and warn fellow technicians and investors that plotting volume isn't black and white. The easiest and simplest view is of course the unaltered sequential volume. This is illustrated in graph 3. The construction of graph 3 is simply to sum the volumes from each of the XAU component issues and plot the daily total. The volumes used were the end-of-day US aggregate of all exchanges that included all pre-market, RTH, and after-market trading. When the index changes the volume is merely the sum of the new components and no adjustments are made to the previous entries in the series. This requires the least amount of work and is the norm within the industry. The problem however is that when the index changes it can introduce artifacts. This time it increased the number of issues in the index and therefore volume increased due to there being twelve stocks in the index versus eleven the day before. This of course gives the appearance to a swing trader that volume is increasing with higher highs and produces a buy signal. It also gives rise to the false conclusion that there is more demand at higher prices. And yet, I wonder how many technician noticed this artifact. Ultimately, this could be the proper interpretation of the chart, but the artificially induced spike in volume creates a logical flaw in reasoning and is hard to ignore. It seems that this is one of those instances when applying a little common sense could help to avoid a bad trade.
So what would the chart look like if the volumes were recalculated using the new index's composition of twelve stocks. This is illustrated in graph 2. This chart required a little more work, but even with the aid of a computer, it's still difficult. This obstacle is precisely why many within the field ignore volume. It's messy and there hasn't been much discussion as to which method is better at producing profits. So instead of knowing that the volume was artificially inflated by a change in the index, most technicians mistakenly view the increased volume and recite to their clients that there's greater demand by investors because of the increased volume. This view is easily discredited as you view graph 2. You can clearly see that when the volume from twelve stocks is now compared, the previous high wasn't met with increased demand but rather with less.
However given this new information, how is one to decide how to interpret the swing high? Could there be another formula for us to consider? The answer is yes. There is another formula for us to consider. The obvious problem with graph 2 is that the prices don't reflect all twelve stocks prior to the index change. Prior to 8/18/03 there were only eleven stocks in the index and after that date there are twelve. So this method creates another artifact that skews the volume of the past. By recalculating all of the volume data in the series to include twelve stocks, it removed the artifact from the previous high but it alters the relationships of previous highs and lows by including volume data that didn't exist at that time. Despite the added work, this method helped us to understand that the volume at the current higher high (8/20/03) didn't expand, but it introduced a different kind of error.
As some of you know, the XAU is a capitalization weighted index which means that both the price and the number of shares outstanding determine the value of the stock. So price alone isn't how the index is computed. By using market capitalization, the total value of the company is represented in the index and not just its price. This has the benefit of equalizing price changes and it doesn't skew the index's movement to the higher priced stocks. However, larger companies do influence the index more than smaller companies and currently NEM is the largest company in the index. It alone represents nearly 26% of the index's value as of 8/22/03. (current XAU components listed at: http://www.phlx.com/products/sectors/xaucomp.htm ) The reason for delving into this detail is because it gives rise to yet another formula to apply in creating the index's volume. Currently, the Philadelphia exchange doesn't post a volume for the index and nobody else is posting a total volume figure other than this site which has been summing the component issues' volumes.
Graph 4 is a capitalization weighted volume figure and its calculations are the most complex. And besides being the most complex, this volume figure is difficult and timing consuming to compute because it is dependent on several sets of data. Before one can begin calculating this figure, you need to know the complete history of changes to the index. In addition to the database of component issues, you need to know the shares outstanding and when the Philadelphia exchange applied those changes to the index. If that wasn't enough to stop you from calculating this, then you need to find daily quotes for delisted companies and companies that no longer exist. These companies may have gone bankrupt or were acquired. In either case, finding stock quotes for inactive companies is not easy. Aside from finding quotes from inactive companies, you'll need quotes for the current companies. After you have gathered these, your database will now include: 1. a chronological list of index components, 2. a chronological list of shares outstanding for 24 companies, and 3. stock quotes for 24 companies.
The calculation for graph 4 is completed in steps. First, determine the list of stocks in the index for that day. Second, determine the number of shares outstanding on that day. Third, get the closing price for each stock for that day, and fourth, get the volume for each stock that day. Once these steps are completed the formula for creating the capitalization weighted volume figure is easy. The next step is to calculate the market capitalization and that is computed by multiplying the closing price with the stock's supply of stock, the shares outstanding. The daily market capitalizations for each stock in the index are then summed to create a total market capitalization for the index. Then the stock's market capitalization is divided by the index's total market capitalization to compute the stock's weighting. This is simply a fraction of the whole. Think of the XAU as one unit and each stock represents a fraction of that unit. The weighting is that company's value as a proportion of the whole. Then the volume is multiplied by the weighting to compute that company's contribution to the total volume for that day. These computations must be repeated each day and there in lies the difficulty of this volume figure.
The effort required to maintain these databases in not trivial and most technicians are not inclined to do this. Most technicians aren't computer experts nor are they expert at creating and maintaining databases. Regardless, the age of computers has raised the bar in the level of sophistication that all technicians must have with computers and precision is required when determining the validity of a theory. Secondly, thirty years ago our predecessors used a calculator and a pencil to make calculations and they relied on others like Standard & Poor's to update indices. Today trading systems are being formulated daily and computer skills are a necessity for designing your own trading methods. Technicians can no longer totally rely on other providers for information and they can't assume that the information that they're getting is what they think it is (as is the case with the XAU volume reported by Yahoo or Bloomberg). They should not assume anything. They must make inquiries and verify. This critical first step is the only way to improve technical analysis's credibility and integrity.
In summary, graph 2 shows the recalculated volume based on the XAU's latest composition of twelve stocks. In graph 2, the volume is computed by adding the daily volume of twelve stocks every day. Graph 3 shows you the unaltered sequential total volume of the XAU's underlying component issues for that day. In graph 3, the volume is computed by adding the daily volume of the XAU's components on that day, and in graph 4, the weighting is subject to change every day based on the supply of stock and the closing price for each stock. Graph 4 shows you the capitalization weighted volume for the XAU.
Notice that the amount of volume is different for all three graphs. In graph 1, the XAU penetrated the previous high on 8/19/03 and broke out above the previous high set on 8/14/03. If you're a Wykoff swing trader then graph 2 tells you that the 8/19/03 high occurred on slightly less volume. But if you look at graph 3, the volume depicted shows a dramatic increase in volume (remember there are now 12 stocks comprising the total whereas the week before there were only 11 stocks). If that wasn't confusing enough, look at graph 4 and it shows a similar view but notice how the total volume is reduced by a factor of 10. In graph 2 and 3 the volumes are in the 30 million range while the daily total in graph 4 is in the 3 million range. This is the result of multiplying each stock's daily volume by its weighting factor, which is a fraction.
So which of these is correct? Unfortunately, this small sample isn't adequate to determine which yields more profitable signals, but it serves to highlight how and why various technicians can produce different results. As a matter of fact, even the capitalization weighted volumes could be subject to a different set of calculations. Or if one wanted you could even calculate the index's volume based on the ratio of turnover. In that case, the weighting would be calculated using stock's shares outstanding as a proportion to the total number of shares outstanding in the index. In this case, neither price nor market capitalization would be part of the computations. The stock's total daily volume would be multiplied by this alternative weighting factor and this would represent the company's supply of stock as a fraction of the index's total supply of stock. This appears to be the most rational choice since the weighting is dependent only on the index's total supply of stock. Price is not included in the weighting factor for volume and that appeals to technicians as they view price and volume as separate entities. This view is depicted in graph 5 as the fractional supply volume. However, despite its logical appeal, this method introduces artifacts that can be avoided if one uses the market capitalization weighted volume.
Another artifact that introduces judgement is with regards to pre-holiday trading days. Some of these are half-days, or early closes, and these induce another artifact and ambiguity among technicians. Some technicians expand the volume by a multiplier so that the volume is expanded to represent a full day while others do not. So yet another data series could be created if the volume were adjusted for these half-days. This gives us our fifth method for calculating volume.
Stock splits are another messy detail that must be resolved when determining the daily volume, but this artifact is eliminated when using the market capitalization method. A stock split does introduce an artifact when adding the individual stock's volumes or when using the fractional supply method, but it doesn't with the market capitalization weighted volume. For example, if a company has a 2 for 1 split, the shareholder will get two shares for every one they own. So the company doubles the shares outstanding to account for this and the stock price drops in half. In the end, the net effect is that the company's value stays the same. So the market capitalization weighting remains the same and there is no effect of the stock split on the weighting factor. But this isn't the case when the volumes are simply added, or the factional supply method is used. In these cases, an artifact is introduced. When the volumes are simply added, a dramatic change in the company's daily volume as a result of the stock split is passed directly through to the index's total daily volume. This appears as a spike in volume. When the fractional supply weighting is used, the stock split alters the total shares outstanding and the change in the shares outstanding alters the company's weighting factor. The new weighting factor introduces an artifact as a result of changing the company's proportion of the index.
But increases in a stock's shares outstanding that do not accompany a stock split can introduce an artifact that technicians aren't familiar with. There are many times when a company increases the total supply of stock and it doesn't perform a stock split. When these events occur, the rankings of the component issues change due a change in the company's total value or market capitalization. This change in valuation then changes the weighting factors and causes an artifact in the volume. So while one method may seem to be more accurate, none of these methods if free from artifacts.
Another artifact that is introduced into market capitalization weighted indices that isn’t so obvious is that the total market capitalization for the index isn’t constant. It is easy to say that today’s volume can be compared to the past, because the weighting factor compensates for changes in company value or stock splits. But the fact that the index’s total value changes over time and that the index is weighted doesn’t imply that the same quantities of volume are being compared. For example, if the exchange would set the total market capitalization for the index to $200 Million and maintain this arbitrary value throughout the history of the index, then, in a bull market, the exchange would need to reduce the number of companies in the index over time. As each profitable company grows in size, its market capitalization would increase and this growth would lead to the company being excluded in the index because its value exceeds the index’s limit. This over time would cause the volume to decrease because fewer companies or smaller companies would comprise the index. The fact that market capitalization weighted indices have no such arbitrary limit lends them to “walking” higher. This upward bias is built into the index and generally ignored. But when a technician is formulating a trading strategy, logical flaws such as this need to be removed from the equation.
Perhaps a sixth method of calculating index volume should be a hybrid. It should be a ratio of turnover. Perhaps indices shouldn’t be represented by volume but rather with value turnover. This turnover ratio would represent the amount of value relative to the index’s total value. For example, each component stock’s value is computed by multiplying the last price by the day’s trading volume (Graph 6). These values for each component are totaled and then the total value traded for the day is computed. This total value traded is then divided by the index’s total market capitalization so that a ratio is created. These daily ratios now represent the same quantity and invite comparison. These are illustrated in graphs 12, and 13. Notice in graph 12 how the raw total value traded in August 2003 seems to be near the Winter 2002 levels, but in graph 13, the proportion of daily value traded is lower at the August 2003 highs than at the previous highs during the Winter of 2002.
This article illustrates to technicians a total of five different methods to calculate volume plus a hybrid method and there are no references in any textbooks as to which method is preferred. The traditional method of creating an unaltered sequential series is the easiest and the least rational method, but it has a strong following for lack of any other alternatives. Hopefully these other methods will be considered by both technicians and data vendors so that future studies will be conducted to verify that one volume series is more profitable than another.
Graph 1 - XAU end of day prices
Graph 2 - Revised Volume
Graph 3 - Unaltered Sequential Volume
Graph 4 - Capitalization Weighted Volume
Graph 5 - Fractional Supply Weighted Volume
Graph 6 - XAU Daily Total Value Traded (Volume x Price)
Volume Data Correlations
As a curiosity, scatter plots were created to see if one set of volume data was more highly correlated than another. As you can see below, the highest correlation was between the market capitalization weighted volume and the fractional supply weighted volume. This makes sense since the difference between these two is the multiplicative affect of price. The next highest correlation was between the unaltered sequential volume and the revised volume data. Both of which were simply a function of adding daily volumes. However when comparing the correlation of these two against the market capitalization weighted volume, the unaltered sequential volume was more highly correlated than the revised volume. This makes sense since the unaltered sequential volume was based on eleven stocks until the index changed to 12 stocks whereas the revised data contained volume from 12 stocks, one of which wasn't in the index prior to 8/18/03.
In addition, when comparing graph 6 to graph 10, it appears that the correlation for the fractional supply weighting is higher than the market capitalization weighting when compared against the traditional unaltered sequential method.
Although this small sample isn't statistically significant, empirically the observations made here show that it is possible at times for one of these data sets to produce conflicting signals and that technicians should consider testing these different volume sets to optimize their trading systems. As for a definitive decision as to which is the best set of volume data; that is as always a matter of debate. The fractional supply weighted volume has a higher correlation than does the market capitalization weighted volume, but the others are easier to compute and show a strong correlation. And although the fractional weighted volume makes sense, it is prone to introducing artifacts when any changes are made to any company's shares outstanding. As of this writing, I am waiting for the creators of the Philadelphia Exchange's XAU index to comment on these choices, and hopefully they will share their insight into why one method is superior to another. And perhaps, after reading this you'll share your opinion.
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Graph 7- a scatter plot comparing graph 2 and graph 3
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Graph 8 - a scatter plot comparing graph 2 and graph 4
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Graph 9 - a scatter plot comparing graph 3 and graph 4
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Graph 10 - a scatter plot comparing graph 4 and graph 5
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Graph 11 - a scatter plot comparing graph 3 and graph 5
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Graph 12 – XAU Total Market Capitalization versus the Raw Total Daily Value traded.
Graph 13- XAU Total Market Capitalization versus the Total Daily Value Ratio (relative to the Mkt. Cap.)
Summary
Today we can add another layer of valuable information to indices by creating a volume figure that truly represents the index. And in doing so, this should allow market technicians to consistently apply rules to the index and to the underlying stocks without the aid of fudge factors. Theories then can be subjected to both the micro and macro view, and be validated or discarded as worthless. In either case, a more meaningful effort can be made to advance the frontiers of financial forecasting through the use of technical analysis when the details are not ignored.
This exploration into how one could compute the XAU index's volume five different ways, describes in detail how to calculate these various volumes for an index. This in no way implies that this is a complete list of all variations, but it does serve as an initiation into exploring more complex computations. As a matter of fact, you could easily multiply these five methods into 20 just by considering using exchange specific volume, pre-market volume, after-market volume, RTH, etc. Plus there may be other formulations yet unknown to the author.
This article doesn't recommend one method over another because these various volumes can be considered optimizations, and rationalizations as to which is best is secondary to the real test - profitability. Logically, the fractional supply weighted volume makes the most sense for the XAU but it may not yield the most money when back-tested. Ultimately, the best volume set will depend on the trading system that the analyst designs and not what is most convenient. However as the correlations shown depict, the easiest method may not be the best, but it's a start towards adding another layer to one's trading system.
Investors and clients demand performance, and these seemingly subtle variations are optimizations that can affect their total investment return. So why wouldn't you consider exploring these variations as any other parameter? It is interesting that many technicians spend countless hours optimizing moving averages and other indicators in search of the best parameters, and yet they do not consider verifying their volume data; much less optimizing it. When the goal is to find the widest application of a profitable rule and to exploit it, then volume should be included in that search for the best variation.
This article hopefully illustrates that technicians can similarly optimize their volume information, and rationally contend with artificially induced artifacts. In so doing, they can produce more stringent rules with fewer exceptions. And although this article analyzed the XAU, these methods for optimizing volume can easily be applied to any other index, such as the S&P500. In addition, hopefully technicians will be more precise in their data selection, identification, and classification. so that they can avoid the pitfalls of assuming that their data is accurate and making erroneous conclusions or false claims. Lastly, if data vendors are looking for ways to improve service, then labeling data and accurately defining it would be a simple improvement. As for market technicians, it behooves you to verify data before expending any effort analyzing it. This will speed up the evolution of your ideas and prevent you from making erroneous conclusions. In addition, properly identifying data will assist other technicians in understanding how your methods were applied so that they can test and verify your results. If these basic scientific rules of experimentation are applied, then technical analysis can advance like any other discipline.
created 8/24/03, ©2003, The Small Investor's Software Company. All rights reserved.
